System and method for gaussian process enhanced GNSS corrections generation

Abstract

A system and method for generating a set of GNSS corrections using a GNSS corrections model comprising a Gaussian process.

I claim: 
     
       1. A method for determining a mobile receiver position comprising:
 receiving, from a set of reference stations, a set of satellite observations; and 
 generating a set of GNSS corrections using a set of Gaussian processes, wherein inputs to the set of Gaussian processes comprise a set of covariance functions relating undifferenced and uncombined satellite observations from the set of satellite observations, wherein the set of covariance functions comprise:
 a covariance function relating satellite orbit errors between two satellite observations, comprising: a constant function combined with a squared exponential function combined with an Ornstein-Uhlenbeck function; 
 a covariance function relating hardware bias between two satellite observations, comprising: a squared exponential bias function combined with an Ornstein-Uhlenbeck function; 
 a covariance function relating clock errors between two satellite observations comprising an Ornsten-Uhlenbeck function; and 
 a covariance function relating atmospheric delays comprising a squared exponential function; 
 
 
       wherein a mobile receiver receives a second set of satellite observations, corrects the second set of satellite observations using the set of GNSS corrections; and determines the mobile receiver position using the set of corrected satellite observations. 
     
     
       2. The method of  claim 1 , wherein the covariance functions relating atmospheric delays comprises:
 a radial covariance function relating a first pierce point associated with a first satellite observation and a second pierce point associated with a second satellite observation comprising a squared exponential function based on a great circle distance between the first pierce point and second pierce point; and 
 an altitude covariance function relating an altitude of the first pierce point and an altitude of the second pierce point. 
 
     
     
       3. The method of  claim 1 , wherein one or more hyperparameters associated with at least one of the covariance functions is determined by:
 selecting a set of tuning hyperparameters and a tuning dataset of satellite observations; 
 predicting a set of predicted GNSS corrections using the set of tuning hyperparameters; 
 comparing the set of predicted GNSS corrections with a set of subsequently determined actual GNSS corrections; and 
 storing a tuning hyperparameter of the set of tuning hyperparameters that predicted the actual GNSS corrections above a threshold accuracy. 
 
     
     
       4. The method of  claim 1 , wherein the set of satellite observations comprises at least 1,000 satellite observations. 
     
     
       5. A method for generating GNSS corrections comprising:
 receiving, from a set of reference stations, a set of satellite observations corresponding to one or more satellites of one or more satellite constellations; 
 generating a set of GNSS corrections using a GNSS corrections model, wherein the GNSS corrections model comprises a Gaussian process, wherein inputs to the GNSS corrections model comprise undifferenced and uncombined satellite observations from the set of satellite observations; 
 constraining a GNSS correction associated with a first time and a GNSS correction associated with a second time to ensure a smooth transition between the GNSS corrections between the first and second time; and 
 determining a position of a GNSS receiver based on the set of GNSS corrections and a set of satellite observations received by the GNSS receiver. 
 
     
     
       6. The method of  claim 5 , further comprising estimating an atmospheric delay at each reference station of the set of reference stations using a precise point precision (PPP) filter, wherein the inputs to the GNSS corrections model further comprise the atmospheric delay at each reference station of the set of reference stations. 
     
     
       7. The method of  claim 6 , wherein estimating the atmospheric delay at each reference station comprises modelling a total electron content of the ionosphere with a multi-shell model. 
     
     
       8. The method of  claim 7 , wherein a covariance function relating a first pierce point associated with a first satellite observation of the set of satellite observations and a second pierce point associated with a second satellite observation of the set of satellite observations depends on a great circle distance between the first and second pierce points of a single shell of the multi-shell model. 
     
     
       9. The method of  claim 7 , wherein a covariance function associated with the Gaussian process comprises a sum of:
 a covariance function relating the satellite observations received at each reference station; 
 a covariance function relating satellite observations received from each satellite; and 
 a covariance function corresponding to a convolution between covariance functions associated with each shell of the multi-shell model, wherein the covariance functions associated with each shell of the multi-shell model corresponds to an altitude covariance and a radial covariance. 
 
     
     
       10. The method of  claim 5 , wherein the set of GNSS corrections are generated without using a Kalman filter. 
     
     
       11. The method of  claim 6 , wherein a covariance function relating a first pierce point associated with a first satellite observation and a second pierce point associated with a second satellite observation comprises a squared exponential function. 
     
     
       12. The method of  claim 5 , wherein the Gaussian process comprises a sparse Gaussian process, wherein the sparse Gaussian process comprises a set of inducing points, wherein the set of inducing points are associated with variables of the set of reference stations. 
     
     
       13. The method of  claim 12 , further comprising rebasing the set of inducing points by:
 calculating a posterior prediction associated with a second set of inducing points; and 
 scaling a prior associated with the set of inducing points based on the posterior prediction. 
 
     
     
       14. The method of  claim 5 , further comprising identifying one or more outliers in the set of satellite observations and removing the outliers from the set of satellite observations. 
     
     
       15. The method of  claim 14 , wherein identifying the outliers comprises identifying the outlier using a random sample consensus (RANSAC) method. 
     
     
       16. The method of  claim 6 , wherein the set of GNSS corrections are operable to correct for at least one of: satellite clock error, satellite orbit error, satellite hardware bias, satellite antenna phase windup, phase center offset (PCO), phase center variation (PCV), solid earth tides, solid earth pole tides, ocean tidal loading, ionosphere delays, troposphere delays, receiver clock error, receiver hardware bias, receiver antenna phase windup/PCO/PCV, carrier phase ambiguity, and multi-path effects. 
     
     
       17. The method of  claim 5 , further comprising determining a parameter of the GNSS corrections model by:
 selecting a set of tuning parameters; 
 predicting a set of predicted GNSS corrections using the set of tuning parameters; 
 comparing the set of predicted GNSS corrections with a set of subsequently determined actual GNSS corrections; and 
 storing a tuning parameter of the set of tuning parameters that predicted the actual GNSS corrections above a threshold accuracy. 
 
     
     
       18. The method of  claim 5 , further comprising validating the GNSS corrections by:
 selecting a set of validation satellite observations, wherein the set of validation satellite observations are not used to generate the GNSS corrections; 
 estimating a GNSS correction associated with the set of validation satellite observations based on the GNSS correction model; 
 when a residual associated with the GNSS correction associated with the set of validation satellite observations is less than a threshold, validating the GNSS corrections. 
 
     
     
       19. The method of  claim 5 , wherein constraining the GNSS corrections at the first and second time comprises constraining a mean quantity of satellite observations detected at a master reference station of the set of reference stations to a common value at the first and second times. 
     
     
       20. A method for generating GNSS corrections comprising:
 receiving, from a set of reference stations, a set of satellite observations corresponding to one or more satellites of one or more satellite constellations; 
 generating a set of GNSS corrections using a GNSS corrections model, wherein the GNSS corrections model comprises a Gaussian process, wherein inputs to the GNSS corrections model comprise undifferenced and uncombined satellite observations from the set of satellite observations; 
 constraining a GNSS correction associated with a first time and a GNSS correction associated with a second time to ensure a smooth transition between the GNSS corrections between the first and second time; 
 validating the GNSS corrections by:
 selecting a set of validation satellite observations, wherein the set of validation satellite observations are not used to generate the GNSS corrections; 
 estimating a GNSS correction associated with the set of validation satellite observations based on the GNSS correction model; and 
 when a residual associated with the GNSS correction associated with the set of validation satellite observations is less than a threshold, validating the GNSS corrections; and 
 
 determining a position of a GNSS receiver based on the set of GNSS corrections and a set of satellite observations received by the GNSS receiver.